1. Field of the Invention
The present invention relates generally to the field of seismic exploration and more particularly to methods of processing 2-D and 3-D seismic data. More particularly the present invention relates to a new seismic attribute for seismic trace analysis. Most particularly, the method of the invention uses wavelet transforms to determine statistical parameters to analyze the structure and stratigraphy shown on seismic sections.
2. Description of the Prior Art
In the oil and gas industry, seismic prospecting techniques are commonly used to aid in the search for and evaluation of subterranean hydrocarbon deposits. Typically, the goal of seismic prospecting is to construct a two dimensional (2D) or three dimensional (3D) representation of subsurface lithological formations in order to identify features that are indicative of hydrocarbon accumulations. Seismic prospecting generally consists of three separate stages: data acquisition, data processing and data interpretation. The success of a seismic prospecting operation depends on the satisfactory conclusion of all these stages.
In the first stage of seismic prospecting, namely seismic acquisition, a seismic source, such as, for example, dynamite, is used to generate a downgoing seismic wave field or signal that propagates into the earth and is partially reflected by subsurface seismic reflectors, i.e. interfaces between subsurface lithologic or fluid units that have different elastic properties. The reflected or upgoing wavefield or signals, known as seismic reflections, are detected by seismic receivers located at or near the surface of the Earth, at or near the water surface, or at or near the seafloor. The detected signals are converted into electric signals and are recorded, thereby generating a seismic survey of the subsurface.
In a 2D seismic survey the recording locations are generally laid out in a single straight line, whereas in a three dimensional (3D) survey the recordings are distributed across the surface in a grid pattern. In simplest terms a 2D seismic line can be thought of as giving a cross sectional picture of the earth layers as they exist below the approximate center point between the shot and receiver locations for geology without much distortion. In an area of complex geology the data may not come from the approximate center point. A 3D survey creates a data cube or volume that is a 3D representation of the subsurface. In either case the recorded signals or seismic energy data can then be processed to yield information relating to the subsurface formations identifying such structures as subsurface formation boundaries. The seismic energy recorded by each seismic receiver for each source activation during the data acquisition stage is known as a “trace”.
The seismic receivers utilized in such operations typically include pressure sensors, such as hydrophones, and velocity sensors such as geophones. Utilizing a dual sensor configuration, namely the combination of a geophone and hydrophone, various summation techniques of the two types of wavefield recordings can be utilized to improve the accuracy of a trace. A modern seismic trace is a digital recording of the energy reflecting back from inhomogenities or reflectors in the subsurface. Thus each digital sample in a seismic trace is associated with a travel time or depth and in the case of reflected energy a two-way travel time or depth from the surface to the reflector and back to the surface again. Further the surface location of every trace is carefully recorded. This allows the seismic information contained within the traces to be later correlated with specific subsurface locations. This provides a means for posting and contouring seismic data and the attributes extracted from the data on a 2D or 3D map.
Once the seismic trace has been acquired, it is then processed during the second stage of seismic prospecting. Seismic processing may involve various techniques to improve the signal to noise ratio, shape the wavelet through deconvolution, gaining the data to reduce the effects of spherical divergence and attenuation, properly positioning the reflected energy by migration, etc. Seismic processing typically involves the use of various mathematical algorithms that are applied to the data to enhance its signal content and to render the data more amenable to interpretation.
One of the main objectives of the data processing stage is to remove, or at least attenuate, unwanted recorded energy, or “noise”, that contaminates the primary seismic signal. Those skilled in the art understand that there are many ways to improve the signal to noise ratio of the seismic data. For example, frequency-wavenumber (F-K) filtering can be used to filter organized noise. Radon transforms can be used to attenuate unwanted multiple energy, i.e., energy that has traveled more than one path in the subsurface. Random noise also can be attenuated by such processes as diversity filtering, Fourier filtering, Karhunen-Loeve transforms, etc. Deconvolution can eliminate reverberations and can increase the resolution of the wavelet. Spiking deconvolution attempts to collapse the seismic wavelet into a spike. Predictive deconvolution permits a certain portion of the wavelet pass without deconvolution, i.e. the lag, but then deconvolves a time window outside of this lag. This predictive deconvolution is generally a milder form of deconvolution but can, with a suitable choice of parameters, be the equivalent of spiking deconvolution.
Likewise, a gain function may be applied to the seismic trace. As a seismic wave travels through the earth, it loses amplitude by two main means: spherical divergence and attenuation. Spherical divergence is caused by the spreading of energy over a larger area as the wave expands. Attenuation is created by the wave moving pore fluids or generating heat as, for example, in the rock matrix. Both these processes can be ameliorated by applying a gain function to the seismic trace. This raises the amplitude of the trace at later times. There are several forms the gain function may take, e.g. tn where n is a user supplied parameter, db per second, etc. The purpose of these corrections is to apply an increase of amplitude with time or depth.
Another method for attenuating unwanted noise components in seismic data traces is through the common-midpoint (CMP) “stacking” process. According to the CMP method, recorded seismic data traces are sorted into common-midpoint groups, called CMP gathers, each of which contains a number of different seismic data traces having the same midpoint but different source-to-receiver offset distances. CMP gathers for a particular point are summed or “stacked” together yielding a single stacked data trace for the point, this trace being a composite of the individual seismic data traces in the CMP gather. Through stacking of CMP traces, the unwanted energy on any one trace is reduced when the trace is added with other CMP traces, such that the desired energy is enhanced. Typically, the stacked data trace has a significantly improved signal-to-noise ratio compared to that of the unstacked seismic data traces.
Prior to creation of a final stack from processed unstacked CMP data, the data must have normal moveout correction (NMO) applied. In NMO correction the CMP data is flattened, i.e. the different reflectors are aligned in time or depth across the unstacked CMP. The standard formula used to do this isTx2=T02+x2/v2 orT02=Tx2−x2/v2 which is the equation for NMO out to the second order. This equation can have further orders such as x4, x6, etc. Most commonly, however, terms on the order of x4 or less are utilized. In the formula above, T0 is the time at zero offset of a reflector, Tx is the time at offset x, “x” is the shot to receiver distance and “v” is the velocity of the medium. In applying the NMO equation, the term x2/v2 term or higher order terms are subtracted from the equation to bring all the data back to a constant T0. The velocity is very important in this determination because the reflectors have to be aligned correctly for the stacking process. The stacking process essentially sums across the CMP gathers. That is, the flat lying reflectors after NMO correction are summed across all the offsets, the distance between shot and geophone. This creates a stacked section, i.e. one trace at each CMP location.
Stacking after NMO need not be the final step in seismic data processing. Additional procedures can be applied to the data in the stack format. Such processes include post-stack deconvolution, post-stack migration, gaining of the data, signal enhancement, etc.
In any event, the foregoing prestack and poststack processes are generally utilized to make the lithologic subsurface section or volume more amenable for interpretation.
To properly position the seismic data for processing, seismic migration is used. Seismic migration moves the unmigrated traces to their correct location or as near the correct location as the particular algorithm permits. Migration improves the seismic data by improving the lateral positioning of seismic reflectors with dip, i.e. reflectors at an angle, the dip, in the subsurface. Migration will move the data updip and will shorten the reflection. Migration also collapses the diffraction hyperbolas to a point such as the beginning of a fault plane. Migration can be prestack or poststack. Prestack migration is preferred but is more expensive as each trace at a CMP, for example, will be migrated. There is also a distinction between time and depth migration. If the subsurface comprises severe velocity changes the more complicated algorithms of depth migration are needed. Prestack and poststack depth migrations will be more expensive than the corresponding time algorithms but in some cases will have to be used.
The final phase of seismic exploration is interpretation. Interpretation uses the seismic section or volume to make an estimation of the subsurface, both structurally and stratigraphically, by identifying reflective surfaces in the subsurface, e.g. reflectors and faults. The resulting form of the subsurface may be used to identify the location of possible hydrocarbon accumulations. This process is referred to as “structural interpretation.” Similarly, a change in the characteristics of a reflector, such as amplitude or phasing, may be indicative of stratigraphic hydrocarbon traps. Most of the interpretations at this time use both poststack and prestack attributes. Amplitudes in poststack or prestack data can be very important as high reflectivity values can be indicative of gas concentrations or oil with a high gas charge. Instantaneous frequency or Fourier analysis can be important because frequency “shadows” sometimes exist under hydrocarbon concentrations. Instantaneous phase can be important as it enhances the continuity of reflectors. Instantaneous amplitude can be important for the change of amplitude with hydrocarbon concentrations.
There are many seismic attributes which can be derived from the data, rendering the data more amenable for interpretation, such as, for example, instantaneous phase, instantaneous frequency, instantaneous amplitude or coherency. Instantaneous attributes are most commonly determined utilizing complex trace creation and analysis. Coherency utilizes cross-correlation between traces. None of the foregoing utilize wavelet transform. Seismic attributes are also derived from prestack data as well. Amplitude Variation with Offset (AVO) attributes illustrate how the amplitude of a particular reflector changes as the offset, i.e., the distance between shot and receiver, changes. There are several AVO attributes, such as gradient, intercept, fluid factor, etc.
Notwithstanding the foregoing, it is well known in the art to apply Fourier transforms to seismic traces in order to identify and filter noise in the traces. It is also known to use an outgrowth of Fourier transforms, namely wavelet transforms, to localize and scale seismic traces to render clearer images of the subsurface structure and stratigraphy with which they are associated.
One method of the prior art utilizes wavelet transforms in combination with the calculation of the Hölder exponent to analyze seismic data. Seismic traces are transformed by means of a wavelet transform where the wavelet used is a Morlet wavelet. From this wavelet transform, the Hölder exponents can be derived. The Holder exponent measures the regularity of seismic trace data by measuring the growth or decay of wavelet transform amplitude across a range of scales for each time point in the data. By definition the Holder exponent is the slope, gradient, of a least squares linear regression on the log-log plot of wavelet transform amplitude vs. scale for every time point.
One drawback to utilization of the Hölder exponent is that the Hölder exponent is subject to noise and thus, can prove to be unstable, or have significant variance. In other words, seismic data with noise can have a large negative impact on an attribute which is based on the slope or gradient of the wavelet transform.
Thus, it would be desirable to provide a seismic attribute for seismic trace analysis that is highly localized, yet that has a high degree of stability with respect to noise.